In general, wandering subspaces of operators on Hilbert spaces play an important role in connection with invariant subspaces (see [1]}, [2]}). The above result is another instance where, the importance of wandering subspace becomes apparent. In other words, it forms a tractable subset of the Hilbert space \(\mathcal {H}\)  that can be used to determine certain pure contractions. Let us give a few more definitions that are required for describing our main result.
